Issue

TROLL model currently compute leaf lifespan with Reich’s allometry (Reich et al. 1991). But we have shown that Reich’s allometry is underestimating leaf lifespan for low LMA species. Moreover simulations estimated unrealistically low aboveground biomass for low LMA species. We assumed Reich’s allometry underestimation of leaf lifespan for low LMA species being the source of unrealistically low aboveground biomass inside TROLL simulations. We decided to find a better allometry with Wright et al. (2004) GLOPNET dataset.

We tested different models starting from complet model Mcomp: \[ {LL_s}_j \sim \mathcal{logN}(log({\mu_s}_j),\,\sigma)\,, ~~s=1,...,S_{=4}~, ~~j=1,...,n_s\]

\[{\mu_s}_j = {\beta_0}*e^{{\beta_1}_s*{LMA_s}_j^{{\beta_3}_s} - {\beta_2}_s*{Nmass_s}_j^{{\beta_4}_s}}\] \[{\beta_i}_s \sim \mathcal{N}({\beta_i},\,\sigma_i)\,^I\] \[(\beta_i, \sigma, \sigma_i) \sim \mathcal{\Gamma}(0.001,\,0.001)\,^{2I+1}\]

LL graph

Figure 1: Leaf mass per area (LMA), leaf nitrogen content (Nmass) and leaflifespan (LL). Leaf mass per area (LMA in \(g.m^{-2}\)), leaf nitrogen content (Nmass, in \(mg.g^-1\)) and leaf lifespan (LL in \(months\)) are taken in GLOPNET dataset from Wright et al. (2004).

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA + {\beta_2}_s*N,\sigma)\,\] Maximum likekihood of 10.0779021 and \(R^2\) of 12.653

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -2.0074706 and \(R^2\) of 13.525

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} + {\beta_2}_s*N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 13.1931018 and \(R^2\) of 15.319

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA + N,\sigma)\,\] Maximum likekihood of 1.0074785 and \(R^2\) of 12.877

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -0.4205913 and \(R^2\) of 13.808

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} + N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 5.7451315 and \(R^2\) of 12.78

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA,\sigma)\,\] Maximum likekihood of 4.2132211 and \(R^2\) of 15.128

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of -6.9667156 and \(R^2\) of 14.27

Convergence

Model

\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of 8.787795 and \(R^2\) of 15.358

Convergence

Results

Figure 3: Model predictions.